I want to know what they believe to be the origin of their morality
I see a sort of layered approach to this.
On one level, we mostly deal with morality in terms of impulses; some things just
seem right and wrong to us, with no real need to put much thought into it. Some of this, I think, is natural. We're social animals, so we've evolved with certain instinctual impulses that help us survive as a species. We can see some of this in the way other animals behave (exhibiting altruism, concern for fairness and reciprocity, concern for the well-being of others of the same kind - especially those familiar to us).
Added to that, we have societal norms that are ingrained into us from a young age. These norms are intended to keep peace and allow the society to function and expand, although they don't always work.
Most people seem to only approach morality by allowing themselves to be guided by these impulses, the natural ones they instinctively feel and the ones that reflect the values of the society they've been raised in. And for the most part, that works without ever needing to think about it too much. The problem is that everyone, to some extent or another, will have these impulses overridden by some other desire at some point or another. Usually it won't be anything major, but it happens to all of us. And we also will at some point or another get the feeling that some things that we impulsively think are moral or immoral might not actually be. But what can that mean if nature and society are what dictate our morals?
This is where the philosophical practice of ethics comes in. We try to address these discrepancies by nailing down what it is that makes something "good" or "evil" beyond our/society's/God's say-so. And of course, there are different ways of doing this, and there's lots of room for debate. But there's nothing in this debate that requires a belief in or adherence to any particular concept of God. In fact, that usually makes things murkier than they already are.
